A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)

Abstract

While Eulerian schemes work well for most gas flows, they have been shown to admit nonphysical oscillations near some material interfaces. In contrast, Lagrangian schemes work well at multimaterial interfaces, but suffer from their own difficulties in problems with large deformations and vorticity characteristic of most gas flows. We believe that the most robust schemes will combine the best properties of Eulerian and Lagrangian schemes. In this paper, we propose a new numerical method for treating interfaces in Eulerian schemes that maintains a Heaviside profile of the density with no numerical smearing along the lines of earlier work and most Lagrangian schemes. We use a level set function to track the motion of a multimaterial interface in an Eulerian framework. In addition, the use of ghost cells (actually ghost nodes in our finite difference framework) and a new isobaric fix technique allows us to keep the density profile from smearing out, while still keeping the scheme robust and easy to program with simple extensions to multidimensions and multilevel time integration, e.g., Runge–Kutta methods. In contrast, previous methods used ill-advised dimensional splitting for multidimensional problems and suffered from great complexity when used in conjunction with multilevel time integrators.